Isosceles Triangle Side Calculator
The isosceles triangle side calculator will determine the lengths of an isosceles triangle if you give it the area, the height, the angles, or the perimeter.
Area12
Height to the base4
Area12
Perimeter16
Sides5, 5, 6
Angles53.1301°, 53.1301°, 73.7398°
TypeAcute isosceles
Inradius1.5
Circumradius3.125
Working
| Semi-perimeter s | 8 |
| Area (Heron) | √(s(s−a)(s−b)(s−c)) = 12 |
| Height on side a | 2 × area ÷ a = 4.8 |
| Inradius | area ÷ s = 1.5 |
| Circumradius | abc ÷ 4·area = 3.125 |
| Angle sum | 180° (always 180°) |
The formula
two equal legs, base b: h = √(leg² − (b/2)²)
What always holds
- The three angles add to 180°, without exception.
- Any two sides must add to more than the third — the triangle inequality. Sides of 4, 5 and 12 cannot close.
- The longest side always faces the largest angle.
Area = ½ × base × heightfor any triangle, with the height measured perpendicular to that base.
Which formula to reach for
With three sides, use Heron’s formula. With a base and its height, use ½bh. With two sides and the angle between them, use ½ab·sin C. With a right angle, the two legs are already base and height, so the area is just half their product.